An investigation of transformation-based prediction interval for the Weibull median life

Abstract

Statistical inference based on the Weibull distribution, a distribution widely used in reliability and survival analysis, is usually difficult as it often involves numerical computation and approximation. However, this distribution can be transformed to near-normality by a simple power transformation. Based on this transformation, a prediction interval (PI) for its median can be easily constructed through an inverse transformation. The procedure for selecting the best power transformation through minimizing Kullback-Leibler information is described. The property of this transformation-based PI is investigated. Simple correction factors are also proposed. It is shown that the transformation-based PI with corrections performs well, irrespective of the sample size and parameter values. Simulation results show that the new PI generally outperforms the existing PI. Numerical examples are given for illustration.